Privacy is like virginity, you don't get it back.

There is no way to prevent the retention of digital data by anyone who
has it.  When you make that data public by publishing it, you give it
to anyone who downloads it.  You would be foolish and naive to believe
otherwise.

The X-No-Archive request is a flag to anyone who wants to easily
identify the juicy stuff to archive.  You should assume that if
someone in the future wants to retrieve your post, there will be an
archive somewhere which has it, and you will only have made it easier
to find.  You appear to believe that if you direct someone not to save
your message, then some force of nature will compel them to do that.
As I say, this is foolish and naive.

Crusty Old Curmudgeon